Best coapproximation in L?(µ, X)

Abstract

Let X be a real Banach space and let G be a closed subset of X. The set G is called coproximinal in X if for each x ? X, there exists y? ? G such that

y ? y?

?

x – y

, for all y ? G. In this paper, we study coproximinality of L?(µ, G) in L?(µ, X), when G is either separable or reflexive coproximinal subspace of X.